Universal Hyperbolic Geometry 0: Introduction

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Universal Hyperbolic Geometry 0: Introduction

Hyperbolic geometry, in this new series, is made simpler, more logical, more general and... more beautiful! The new approach will be called `Universal Hyperbolic Geometry', since it extends the subject in a number of directions. It works over general fields, it extends beyond the usual disk in the Beltrami Klein model, and it unifies hyperbolic and elliptic (and other) geometries.This introduction outlines the differences between this course and that found in all the standard textbooks and courses at universities. We avoid ``real numbers'', avoid ``axioms'', avoid transcendental functions such as cos, sin, log, tanh, avoid absolute values. And treat square roots more algebraically. Our approach uses high school algebra, and is essentially projective geometry combined with a distinguished conic---the unit circle in the plane. We will also later see that this approach ties in very closely with the geometry of Einstein's special theory of relativity.The series is developed and presented by N J Wildberger, also the originator of Rational Trigonometry.

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